Modeling diesel combustion with tabulated kinetics and different
flame structure assumptions based on flamelet approachModeling
diesel combustion with tabulated kinetics and different flame
structure assumptions based on flamelet approach Citation for
published version (APA): Lucchini, T., Pontoni, D., D’Errico, G.,
& Somers, B. (2020). Modeling diesel combustion with tabulated
kinetics and different flame structure assumptions based on
flamelet approach. International Journal of Engine Research, 21(1),
89-100. https://doi.org/10.1177/1468087419862945
DOI: 10.1177/1468087419862945
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Modeling diesel combustion with tabulated kinetics and different
flame structure assumptions based on flamelet approach
Tommaso Lucchini1 , Daniel Pontoni1, Gianluca D’Errico1 and Bart
Somers2
Abstract Computational fluid dynamics analysis represents a useful
approach to design and develop new engine concepts and investigate
advanced combustion modes. Large chemical mechanisms are required
for a correct description of the com- bustion process, especially
for the prediction of pollutant emissions. Tabulated chemistry
models allow to reduce signifi- cantly the computational cost,
maintaining a good accuracy. In the present work, an investigation
of tabulated approaches, based on flamelet assumptions, is carried
out to simulate turbulent Diesel combustion in the Spray A frame-
work. The Approximated Diffusion Flamelet is tested under different
ambient conditions and compared with Flamelet Generated Manifold,
and both models are validated with Engine Combustion Network
experimental data. Flame struc- ture, combustion process and soot
formation were analyzed in this work. Computed results confirm the
impact of the turbulent–chemistry interaction on the ignition
event. Therefore, a new look-up table concept Five-Dimensional-
Flamelet Generated Manifold, that accounts for an additional
dimension (strain rate), has been developed and tested, giv- ing
promising results.
Keywords Computational fluid dynamics, combustion modeling, diesel,
Approximated Diffusion Flamelet, Flamelet Generated Manifold,
Five-Dimensional-Flamelet Generated Manifold, Spray A
Date received: 8 March 2019; accepted: 20 June 2019
Introduction
The continuous development of the existing technology of
compression ignition engines requires a deep knowl- edge of the
complex thermal, chemical and fluid dynamics processes that govern
the combustion process to further improve its efficiency and
quality of exhaust gases.1–4 Novel advanced combustion systems as
well as optimal chamber design and fuel injection strate- gies2,5,6
and more efficient after-treatment devices (SCR, LNT, DPF, DOC)7–10
are required to meet the more and more stringent regulations.11
Moreover, potentialities associated with the use alternative fuels,
eventually mixed with the conventional ones, must be well
assessed.12–15 To this end, it is necessary to per- form both
fundamental and applied studies by means of advanced numerical and
computational techniques. The Engine Combustion Network (ECN)16 has
been built over the last decade supported by this motivation:
the creation and availability of large databases with high-quality
experimental results generated at different international
institutions to deep the fundamental understanding of the injection
and combustion process and support the validation and development
of compu- tational fluid dynamics (CFD) combustion models.17
Focusing on Diesel combustion, a large number of experiments were
carried on not only by injecting n- dodecane sprays, chosen as
Diesel fuel surrogate, in a
1Department of Energy, Politecnico di Milano, Milano, Italy
2Eindhoven University of Technology, Eindhoven, The
Netherlands
Corresponding author:
Lambruschini 4, 20156 Milano, Italy.
Email:
[email protected]
constant-volume vessel chamber, recording ignition delays (IDs) and
pressure rise (and hence the rate of heat release rates), but also
collecting quantitative information about the flame structure, such
as lift-off lengths (LOLs) and soot distributions.
Open discussion in the ECN community evidenced the importance of a
detailed chemical mechanism to be employed in the CFD approach to
correctly estimate both global combustion parameters and details of
tran- sient flame structure. However, the Direct integration of
chemistry equations to compute reaction rates is computationally
demanding since it involves a large number of species and the use
of ordinary differential equation (ODE) stiff solvers. For this
reason, the size of the chemical mechanism which can be used in
practi- cal simulations is limited both in terms of species and
reactions.18 An interesting alternative for the reduction of CPU
time is the tabulated kinetic approach, in which the reaction rates
are stored in a look-up table and retrieved during the simulation,
as a function of the thermodynamic state of the system.18–21 The
com- bustion models can then also include the effect of
turbulence–chemistry interaction, for a better predic- tion of
ignition and combustion of Diesel spray.22–24
To this aim, the flamelet approach is widely accepted where
chemical reactions are assumed to take place in an ensemble of
small laminar flames also called flame- lets.25 Objective of this
work is to compare two approaches which are both based on the
flamelet assumption and make us of tabulated kinetics. The first is
called Approximated Diffusion Flamelet (ADF) while the second is
the Flamelet Generated Manifold (FGM). Both the approaches are
analyzed in terms of their capability to predict auto-ignition and
flame stabi- lization process. ADF approach is based on approxi-
mated flamelets, which are computed by employing the Homogeneous
Reactor table.18,26 FGM model consists of storing and retrieving
low-dimensional manifolds created using solutions of
one-dimensional diffusive flames with direct integration of
detailed kinetic chem- istry, by means of the CHEM1D
application:27–29 the thermal state of a reacting spray is
expressed as func- tion of four variables: pressure, ambient
temperature, mixture fraction and progress variable. An extension
of this approach, which was also tested in the current
investigation, consists in a novel model, called Five-
Dimensional-Flamelet Generated Manifold (5D- FGM): the additional
dimension of the table is the applied strain rate. A better
description of the whole combustion process was achieved,
especially for the low reactivity cases, emphasizing the importance
of turbulence–chemistry interaction for a correct predic- tion of
ignition and flame stabilization.
Computational model
Diesel combustion is affected by the complex interplay between
turbulence and chemistry which determines
the auto-ignition time, heat release rate during mixing controlled
combustion and the distance from the nozzle at which the flame
stabilizes (LOL).30 Different approaches to couple turbulence and
chemistry were proposed in the past and they can be mainly
classified in the way chemical kinetics and turbulence–chemistry
interaction are handled. For what regards the computa- tion of the
chemical species reaction rates, it is impor- tant to note that the
two possible solutions are either to use direct integration or to
generate an offline look-up table. Despite the fact that the first
approach is surely more detailed and flexible, it is also
computationally very demanding due to the necessity of employing
stiff solvers with very small time-steps to estimate the chem- ical
species reaction rates. This aspect introduces sev- eral
limitations for the maximum number of species that can be used in
practical simulations and the conse- quent accuracy of the adopted
mechanism. Moreover, accounting for sub-grid mixing and turbulence–
chemistry interaction introduces further computational overheads.
This is related to the integration of the pre- sumed probability
function, or the transport of many species and energy equations
such as the number of simulated flow realizations or stochastic
fields.31
Therefore, tabulated kinetics can offer a possible solu- tion to
reduce the CPU time and to keep an acceptable accuracy. Reaction
rates and chemical composition are stored in a look-up table which
is generated from a chemical mechanism and the assumption of a
certain flame structure like a well-stirred reactor or laminar
diffusion flame.
Figure 1 illustrates how the CFD solvers based on tabulated
kinetics work. Additional transport equations are solved with the
Reynolds-averaged Navier–Stokes (RANS) method for mixture fraction
~Z, mixture frac- tion variance Z
002, progress variable ~C and unburned gas enthalpy ~hu which is
then used to estimate the cor- responding unburned gas temperature
Tu. In case diffusion-mixing effects are considered, the stoichio-
metric scalar dissipation rate ~xst is also computed. The look-up
table is accessed with local cell values of ~Z,
Figure 1. Operation of combustion models based on tabulated
kinetics.
2 International J of Engine Research 00(0)
Z 002, ~C, p, Tu and ~xst, and it provides the chemical com-
position and the progress variable reaction rate to the
solver.
Two different combustion models based on tabu- lated kinetics were
employed in this work: their corre- sponding look-up tables are
generated from laminar diffusion flame calculations. The models
will be referred as ADF and FGM.
The main difference between ADF and FGM is related to the way
reaction rates are estimated during the table generation process.
In the ADF case, they are in turn taken from a look-up table based
on homoge- neous auto-ignition calculations. Reaction rates are
directly computed using detailed kinetics in the FGM table
generation.
ADF table
Purpose of the ADF model is to provide a realistic description of
the turbulent diffusion flamelet: it takes into account
turbulence–chemistry interaction, sub-grid mixing and premixed
propagation, thanks to the scalar dissipation rate x, which
controls the diffusion rate of the species.19,21 Flamelet equations
are solved in the mixture fraction space z in an approximate way,
only for the progress variable and the enthalpy, assuming unity
Lewis number22
r ∂C
∂t = r
∂t ð2Þ
where C is the progress variable, defined as the heat release by
the combustion.19,22 The progress variable source term _C is taken
from a look-up table which is generated from homogeneous reactor
auto-ignition cal- culations.19 To avoid too anticipated ignitions
related to progress variable diffusion, the progress variable
reaction rate is set to zero in when the equivalence ratio f is
higher than 3. ADF table is generated according to user-specified
ranges of unburned temperature Tu, pres- sure p, equivalence
ratio/mixture fraction Z, in addition to the stoichiometric scalar
dissipation rate xst and the mixture fraction segregation factor
SZ. Subsequently, the scalar dissipation rate x, for equations (1)
and (2), is computed according to Peters’ model32
x = xst
exp( 2½erfc1(2z)2) exp( 2½erfc1(2Zst)2)
ð3Þ
To account for the sub-grid mixing, a b-distribution is assumed for
both the chemical composition and the progress variable: the
corresponding values at user- specified mixture fraction table
points are
f t, ~Z,Z00 2
dz ð4Þ
where Z002 values are computed from the corresponding user-defined
mixture fraction variance segregation factors
Z00 2 =SZ
~Z(1 ~Z) ð5Þ
to avoid numerical integration errors which might negatively affect
the model consistency in terms of energy conservation; in case of
very low variances, the b-distribution is approximated with a
d-distribution.
A small time-step is necessary during the ADF table generation
process to correctly account for the com- bined effects of mixing
and reaction (Figure 2). ADF table should be generated with a large
enough range of xst to include extinction, allowing a correct
description of the diffusion flame stabilization process.
Solving the flamelet equations with tabulated kinetics introduces
an approximation with respect to the case where detailed chemistry
is used. To this end, authors have performed in Lucchini et al.18
constant- volume vessel spray combustion calculations with the
representative interactive flamelet model using a single flamelet
with both detailed and tabulated kinetics. Similar results were
found for both the approaches, with the largest difference noticed
for conditions of low ambient oxygen concentration.
FGM table
Unsteady counter-flow diffusion flame calculations with detailed
kinetics are conveniently processed for the generation of the FGM
look-up table (Figure 3). Computed results are parameterized as
function of the mixture fraction Z and the progress variable c: a
low- dimensional manifold is generated considering the solu- tion
of unsteady one-dimensional flamelet equations in the physical
space28,29,33
Figure 2. Generation of the ADF chemistry table.
Lucchini et al. 3
∂s
l
cp
∂h
∂s
ð8Þ
where s is the spatial coordinate perpendicular to the flame front,
D is the diffusion coefficient and K is the flame stretch rate.
This last variable has a large influ- ence on the mass burning
rate: it is defined as the rela- tive rate change of mass contained
in the infinitesimal volume33
K= 1
dt ð9Þ
The flamelet stretch field K is computed from the transverse
momentum equation
∂ruK
∂x =
2rK2 + rua
2 ð10Þ
a denotes the applied strain rate at the oxidizer side and it is
related to the velocity gradient. Equations (6)–(8) are solved by
means of the CHEM1D tool. The user specifies the boundary
conditions, namely Tu, Tfuel, p, a, air and fuel composition.
Computed results are post- processed and stored in a look-up table
by means of a MATLAB script.29
The progress variable source term and the chemical composition are
determined as a function of c. Differently from the ADF model, the
progress variable is defined as a linear combination of chemical
species, which are assumed to be able to describe the whole
combustion process, from ignition, low- and high- temperature heat
release phases and eventually the fully established diffusion
flame
C=2:70YHO2 +1:50YCH2O +0:9YCO +1:20YH2O
+1:20YCO2 ð11Þ
The FGM table is generated by post-processing the results provided
by CHEM1D simulations. During such stage, the user specifies the
table discretization in terms of mixture fraction Z and progress
variable c. The FGM combustion model considers only one strain rate
and it does not account for sub-grid mixing for the
estimation of the chemical composition in the computa- tional
cells.
5D-FGM table
The 5D-FGM is a new concept developed in the con- text of this work
with the main purpose to improve the prediction of the ID and flame
stabilization process. The 5D-FGM table is generated by processing
results of flamelet computations with multiple strain rates per-
formed with CHEM1D. To be used in the CFD solver, the strain rate
is converted into the stoichiometric sca- lar dissipation rate by
means of Peters’ model32
xst = a
2
ð12Þ
The MATLAB script is employed for post- processing the flamelets.
Accordingly, the table grows of one dimension, as reported in the
variable hierarchy map, Figure 4.
Experimental validation
The Spray A experiment, which was widely studied in the context of
the ECN,16 was used to validate the pro- posed combustion models.
n-Dodecane fuel is delivered through a single-hole nozzle in a
constant-volume ves- sel with a cubic shape where optical
accessibility is ensured by sapphire windows. Different measurement
techniques allow to gather information regarding the flame
structure, heat release rate, LOL and soot distri- bution.6,34
Simulations were carried out in a two- dimensional computational
mesh with the RANS tech- nique. The average mesh size was 0.5mm
which was further reduced to 0.2mm in the nozzle region. In all the
simulated operating conditions, the injection pres- sure and
duration were set to 150MPa and 5.5ms, respectively. The injection
profile of the 210370 nozzle was used in CFD
simulation.35n-Dodecane oxidation chemistry is modeled using the
mechanism proposed by Yao et al.,36 which includes 54 species and
269 reac- tions. Table 1 reports the main details of the
simulated
Figure 3. Generation of the FGM chemistry table.
Figure 4. Hierarchical tree map of the five variables in 5D-
FGM.
4 International J of Engine Research 00(0)
operating conditions: different ambient temperatures and oxygen
concentrations were considered when keep- ing the vessel density to
a constant value of 22.8 kg/m3.
A summary of the applied sub-models for Spray A simulation,
turbulence and soot assessment is illustrated in Table 2.
Simulations were carried out using the standard ke turbulence model
with the round jet correction (C1 =1:5). For assessment of spray
and turbulence models, non-reacting conditions were first
considered with the same ambient temperature of 900K used in the
so-called baseline condition. Figure 5 shows that computed vapor
penetration results are in rather good agreement with experimental
data. Such result is a fun- damental pre-requisite for a successful
simulation of the combustion process. Further validation under non-
reacting conditions was reported in D’Errico et al.22
Four chemistry tables have been generated, one for each analyzed
oxygen concentration, Table 3 reports the table discretizaion which
represents a good tradeoff between accuracy, computational time and
memory consumption. The stoichiometric scalar dissipation rate
values follow a logarithmic curve and any further increase in xst
resolution does not significantly improve the quality of the
results.
For what regards the FGM combustion model setup, since the
simulation of the flamelet is very time- consuming (direct
integration of the chemistry), and to avoid computational memory
issues, a lower number of discretization points in temperature and
pressure have been selected, and the applied strain rate has been
assumed to a fixed value equal to 700 s–1 (Table 4). In previous
studies, such value was generally found close to the
LOL.38,39
The baseline condition (O2 =15%, T=900K and ramb=22:8 kg=m3) was
first considered to analyze
ADF and FGM results. In particular, Figure 6 com- pares the
computed heat release rate (RoHR) with the apparent experimental
value. Heat losses were not included in CFD simulations and this is
the reason why the computed data overestimate the experimental
ones. Figure 6 illustrates that both ADF and FGM models correctly
describe the main features of the Diesel com- bustion
process.
Three events can be clearly detected:
Ignition, corresponding to the RoHR peak; Mixing controlled
combustion phase, where RoHR
reaches an almost stable value; Burnout, corresponding with the
drop of RoHR.
The ADF model better predicts the ID time, heat release rate
transition from auto-ignition to mixing
Table 1. Simulated conditions for ECN Spray A.
Case O2 (%) Temperature (K)
Baseline 15 900 Low-T 15 850 High-T 15 1000 O2-13 13 900 O2-21 21
900 Non-reacting 0 900
Table 2. Sub-models used on diesel spray simulations.
Phenomenon Model
Turbulence Standard ke Spray evolution Eulerian–Lagrangian Spray
breakup Kelvin-Helmholtz &
Raileigh-Taylor Droplet heat transfer Ranz–Marshall Evaporation D2
law + Spalding mass number Scalar dissipation rate Peters Soot
Leung et al.37
Figure 5. Non-reacting case: vapor penetration for ADF and
experimental data; uncertainty is highlighted with green
shadow.
Table 3. ADF table discretization.
Variable Number of points Range
Temperature (K) 21 750–1250 Pressure (bar) 3 40–80 Mixture fraction
(–) 53 0–1 Normalized progress variable (-)
91 0–1
Mixture fraction segregation (–)
7 0–1
Table 4. FGM table discretization.
Variable Number of points
Range
Temperature (K) 5 800–1050 Pressure (bar) 3 50–70 Mixture fraction
(–) 371 0–1 Normalized progress variable (–) 551 0–1
Lucchini et al. 5
controlled combustion and duration of the burnout phase. This
aspect is probably related to the fact the ADF includes the effects
of sub-grid mixing. Figure 7(a) and (b) compares the FGM and ADF
models dur- ing the auto-ignition process in the temperature-
mixture fraction plane. Time evolution of the most reactive mixture
fraction conditions is illustrated with the black line while the
red circles show temperature- mixture fraction scatter plot after
auto-ignition. For both the models, the ignition is predicted at
the side interface between spray and ambient air, and then the
kernel moves burning the premixed fuel underneath. However, in FGM,
the intermediate temperature reac- tions occur at richer mixture
fraction location (as depicted in Figure 7(b)). To avoid a too
anticipated ID, in all the ADF simulations, the reaction rate was
set to zero for f . 3 and this is the reason why temperature
clearly drops down at Zmax=0:124 in Figure 7(a).
FGM and ADF flame structures are compared in terms of scatter plots
of OH, formaldehyde and acety- lene mass fraction as function of Z.
The magnitude of YCH2O between the two combustion models is
similar, but the location of the peak is different, more toward
rich mixture (near the injector) in case of FGM as shown in Figure
8(a). The main reason is the limitation of progress variable source
term in case of ADF. Both models predict a correct location of the
OH peak close to the stoichiometric mixture fraction value.
However, inclusion of sub-grid mixing via mixture fraction var-
iance is probably the reason for a lower maximum OH value for ADF
combined with a larger portion of the mixture fraction space where
OH was found. A similar behavior can also be found for the C2H2
mass fraction as it can be seen from Figure 8(c).
Flame LOL and ID time were selected as combus- tion indicators for
the validation of the proposed com- bustion models under the
selected operating conditions reported in Table 1. Following ECN
defini- tions,16 the LOL is computed as the axial distance between
injector orifice and the first location where Favre-average OH mass
fraction reaches 14% of its maximum in CFD domain; the ID time is
identified by the instant where maximum temperature rise rate
reaches the highest value. Effect of ambient tempera- ture on ID
and LOL is presented in Figure 9. The ADF model is not fully
capable to provide good rep- resentation of LOL, especially at low
temperature. Shorter value computed with ADF seems to be related to
the diffusion of the progress variable leading to a faster
stabilization: a possible reason for such discrepancy might be
related either to the use of approximate flamelet equations in the
table genera- tion process or in the progress variable definition.
Predicted LOL is very important for the computed soot distribution
since it determines the
Figure 6. Baseline comparison of RoHR: ADF, FGM and experimental
data.
(a) (b)
Figure 7. Red points: scatter plot of maximum temperature as
function of mixture fraction; the black like illustrates the
evolution of the maximum temperature during the intermediate and
high temperature reactions: (a) ADF and (b) FGM.
6 International J of Engine Research 00(0)
amount of rich mixture which burns producing soot precursors.
Effects of oxygen concentration on combustion indi- cators are
reported in Figure 10. Both the models
correctly predict an increase of LOL and ID time when reducing the
O2 concentration at 900K ambient tem- perature. Computed ID times
from the ADF combus- tion model are in better agreement with
experimental data while the LOL is slightly underestimated.
Results from Figures 9 and 10 illustrate that the ADF model better
estimates the ID compared to FGM probably because it accounts for
mixing effects via xst. A correct prediction of ID is rather
important, mainly in the case of engine operation under kinetically
con- trolled combustion modes such as premixed charge compression
ignition (PCCI) and reactivity controlled compression ignition
(RCCI).
To investigate how stoichiometric scalar dissipation rate affects
the auto-ignition process, in Figure 11, the state of mixing
Z
002 and reaction progress c was reported as function of the
stoichiometric scalar dissi- pation rate xst before auto-ignition
for all the cells with f=2 which was identified as the most
reactive equiva- lence ratio. Two different ambient temperatures,
850 and 1000K, were investigated. Ignition is possible only at low
xst due to the lower mixture reactivity in the 850K ambient
temperature condition: the maximum progress variable is found in
the stoichiometric scalar
(a)
(c)
(b)
Figure 8. Comparison between FGM and ADF models using scatter plots
of the most important chemical species used to describe the
combustion process: (a) CH2O, (b) OH (b) and (c) C2H2. Results are
reported at 4 ms after start of injection.
Figure 9. LOL and ID comparison between ADF, FGM and experimental
data for different initial conditions of unburned gas temperature
with 15% O2 concentration.
Lucchini et al. 7
dissipation rate range of 0–10 and then it decreases to zero. For
this reason, ignition is expected to take place at the periphery of
the jet. Reaction rate increases with ambient temperature and this
is the reason why at the 1000K condition it is possible to find
non-zero progress variable values also in the 10–100 range of
xst
and the ignition spots are located closer to the nozzle. This
investigation shows the importance of strain rate inclusion in the
combustion model for a correct predic- tion of the ID.
5D-FGM
The 5D-FGM model was tested over the same condi- tions presented in
Table 1. Inclusion of the strain rate effects is expected to
improve the ID predictions. The
tabulated strain rate interval, following a logarithmic profile, is
displayed in Table 5.
The inclusion of the strain rate effects improves the predictive
capability of the 5D-FGM model. Figures 12 and 13 illustrate that
IDs are better esti- mated for the low reactivity conditions
(Tamb=850, 900K; O2=13%, 15%) where chemical reactions mainly take
place in presence of low strain rates.
No significant improvements are reported for the prediction of the
LOL, since it is mainly affected by high strain rate close to the
nozzle and a reasonable value was already used for the generation
of the FGM table. On the other hand, the high reactivity
cases
Figure 10. LOL and ID comparison between ADF, FGM and experimental
data at constant ambient temperature (900 K) and different O2
concentrations.
χ
Figure 11. Effects of mixing and turbulence for the most reactive
cells right before ignition. Progress variable and mixture fraction
variance are reported as function of the stoichiometric scalar
dissipation rate. The most reactive equivalence ratio is assumed to
be equal to 2.
Table 5. 5D-FGM table discretization.
Variable Number of points Range
Strain rate (s–1) 8 100–2000
Figure 12. ID and LOL comparison between FGM and 5D- FGM, for
different ambient temperatures.
Figure 13. ID and LOL comparison between FGM and 5D- FGM, for
different oxygen concentrations.
8 International J of Engine Research 00(0)
(1000K and 21%) are weakly affected, mainly because they sustain
ignition and burning phases at higher xst, near the nozzle: the
experimental LOL is small for the high reactivity case, indeed. The
LOL is not strongly influenced, comparing FGM and 5D-FGM, and the
trend remains close to the experimental curve.
Only the 13% oxygen case shows the highest differ- ence in terms of
LOL. To investigate the reason for such variation, the combustion
efficiency was analyzed in Figures 14 and 15. The experimental
lower heating value (LHV) of n-dodecane was compared with the one
resulting from the ratio between cumulative heat release and
injected fuel mass in the FGM and 5D-FGM simu- lations. To respect
the energy conservation, the esti- mated LHV must be as much close
as possible to the experimental value. 5D-FGM better fulfills the
energy conservation requirement with respect to the standard FGM
model: the use of a single strain rate is the main reason for the
underestimation of heat release during the end of combustion phase.
The improvement is sig- nificant mainly for the O2=13% condition
and this also explains the reason for a predicted shorter LOL. For
the sake of completeness, the same efficiency analy- sis has been
carried out for the ADF simulations: all the simulated points have
a combustion efficiency higher than 99.50%.
Soot prediction of ADF model
The capability of the proposed combustion approach for soot
prediction was investigated thanks to the avail- ability of soot
volume fraction (fv) maps achieved by means of the diffused back
illumination (DBI) tech- nique.40 The current FGM model
implementation does not include the soot model and for this reason,
only ADF results are shown in this section. Authors expect that
they can also be representative of what could be predicted by the
FGM model, since both the approaches estimate similar species
distribution, ID
Figure 14. Cumulative RoHR comparison between FGM, 5D- FGM and LHV
of n-dodecane, for different ambient temperatures.
Figure 15. Cumulative RoHR comparison between FGM, 5D- FGM and LHV
of n-dodecane, for different oxygen concentrations.
(a) (b)
Figure 16. Soot assessment for the baseline condition (O2 = 15%,
ramb = 22:8 kg=m3): (a) soot mass evolution in time and (b) soot
fraction volume location and concentration at t = 4 ms.
Lucchini et al. 9
times and LOL values. Tuning of the Leung-Lindstedt and Jones (LLJ)
model was carried out for the baseline condition including also the
contribution of O and OH to soot oxidation.41,42Figure 16(a) shows
the cumula- tive soot mass within the optical window for the base-
line condition (O2=15%, ramb=22:8 kg=m3). The onset of soot
production is well predicted, but the slope of the curve during the
inception interval is lower in the CFD model. The soot mass peak is
underestimated in magnitude, but the time when it occurs is fairly
cap- tured. The steady-state value is correctly estimated, as the
time and slope of the curve during the complete oxidation of soot
particles. Figure 16(b) shows that the soot volume fraction
distribution is rather well described by the ADF model. Such
results are not only due to a correct selection of the LLJ model
constants, but also due to a correct estimation of the flame
LOL.
Figure 17 reports the evolution of the soot mass as function of
time for the three different ambient tem- peratures Tamb at 15%
ambient oxygen concentration. The model is capable to reproduce the
increase in soot mass with the ambient temperature. However, com-
puted steady-state mass values are underestimated for the 850K
condition while they are overestimated when ambient Tamb is
increased to 1100K. Such trend is not completely consistent with
the prediction of the LOL which is illustrated in Figure 9.
A possible reason for such discrepancy can be mainly related to the
temperature dependency of the model constants describing the soot
formation. Such observa- tion is confirmed by the results
illustrated in Figure 18, where the soot mass evolution is reported
at 900K ambient temperature for three different tested oxygen
concentrations. Computed results are in rather good agreement with
experimental data. In particular, the highest amount of soot was
formed for the 15% ambi- ent oxygen concentration: under such
condition, the flame stabilizes at a relatively short distance from
the nozzle and there is a reduced amount of O2 available
for soot oxidation. Similar amount of soot mass was found for the
other two conditions. In the O2=21% condition, an increase in
oxygen concentration enhances the soot oxidation rate. Reduction of
O2 to 13% decreases the soot formation rate since the flame
stabilizes at a higher distance from the nozzle compared to the
other two conditions.
Conclusion
Two different Diesel combustion models which both use offline
chemistry tabulation, namely the ADF and the FGM, were compared and
assessed in terms of glo- bal heat release rate indicators and
flame structure by simulating the ECN Spray A experiment in
different conditions, including the variation of ambient tempera-
ture and oxygen concentration. The main difference in the
theoretical assumptions beyond these models is in the way reaction
rates are estimated during the table generation process: in ADF
they are based on homoge- neous auto-ignition calculations while in
FGM unsteady counter-flow diffusion flames are solved. The latter
is obviously much more demanding in terms of CPU time such that in
the conventional model formu- lation a single strain rate is
considered assuming that ID is not affected by it in a relatively
large range of val- ues. In the ADF tabulation, instead the
stoichiometric scalar dissipation rate xst and the variance mixture
fraction Z002 are included to account for turbulence– chemistry
interaction.
Models were tested considering n-dodecane sprays under
constant-volume combustion conditions and considering variation of
ambient temperature and oxy- gen concentration. It was observed how
in general igni- tion occurs in rich region and then the reactions
move toward stoichiometric zones. ADF results are clearly
influenced by the turbulence–chemistry interaction: xst, Z002 and
the reactivity play a fundamental role. The study of the main
combustion tracers has given
Figure 17. Soot assessment as a function of ambient temperature
(line = experimental data; squares = ADF).
Figure 18. Soot assessment as a function of oxygen
concentration.
10 International J of Engine Research 00(0)
significant information about IDs, LOLs and flame structure.
Agreement with experimental data was gen- erally good for both
models, apart for the prediction of the LOL at low temperature
given by the ADF model, probably due to an excessive diffusion of
the progress variable, and for the prediction of the ID under the
same condition for the FGM approach. To improve this aspect, a
novel FGM implementation, 5D-FGM, which also include strain rate
effects, was proposed: ID was better estimated since chemical
reactions occur in presence of low strain rates for such low
reactivity condition.
Finally, a preliminary assessment of the soot distri- bution given
by the ADF model was proposed: qualita- tive trends agreed with the
observed data, but further investigations are required to improve
the quantitative estimations of soot mass, especially when varying
the ambient temperature.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship and/or publica- tion of this
article.
Funding
The author(s) received no financial support for the research,
authorship and/or publication of this article.
ORCID iD
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